Yes. Certainly among Aboriginal Canadians, in my experience, 'cultural past' is the only factor of significance in this business; genetic make-up is inconsequential. If you're a white person adopted by a Native family, and so brought up a Native culturally, then you will be considered Native, for all intents and purposes.

Speaking broadly, generally, acknowledging that there are no doubt exceptions, etc.

Btw, this kind of thing is part of the story of such 'imposters' as 'Grey Owl' and 'Long Lance' - if they wanted to try to learn to be Indians, the Indians didn't mind, and didn't see any great need to expose them ...